Be the death of is generally used as an exaggerated or humorous way of describing the effects of laughter, embarrassment, boredom or similar emotions.

1999 - Chris Dolan - Ascension Day - If her mother ever found out that William Grant was in Glasgow, it'd be the death of her.

be frightened to death

be made very alarmed and fearful - informal

be in at the death

be present when a hunted animal is caught and killed

be present when something fails or comes to an end

catch your death = catch your death of cold

catch a severe cold or chill – informal

a deaths head at the feast = a death's head at the feast

A naked human skull as the emblem of death

the head of the conventional personification of death

I had rather be married to a death's-head with a bone in his mouth.

die a death = die the death

come to an end

cease or fail to be popular or successful

1999 - Linedancer - Our industry must expand otherwise it will die a death with just a few clubs remaining.

do something to death

perform or repeat something so frequently that it becomes tediously familiar

a fate worse than death

a terrible experience, especially that of seduction or rape

1991 - Thomas Hayden - The Killing Frost – He dominated the conversation, holding the Hackett and Townshend women spellbound as he told of how he had broken up a white slave ring in Dublin, and how he had rescued an innocent young girl from a fate worse than death.

like death warmed up

extremely tired or ill – informal

Like death warmed up was originally military slang recorded from the 1930s. The North American version is like death warmed over.